Creep Behavior Modeling of a Marble Under Uniaxial Compression

Abstract

Axial strain-time curves for a marble sample were obtained by performing uniaxial compression tests with step loading. Axial strain rate-time data points were then obtained from the axial straintime curves. One power function and one exponential function were selected from the literature to fit the experimental creep data. Based on the characteristics of the plotted axial strain rate-time data points, one power function and one exponential function were proposed as possible functions to model the creep data. By comparing the goodness-of-fit of the aforementioned four functions through regression analysis, it was found that the two exponential functions fit the experimental creep data better than the two power functions. The two exponential functions showed very close goodness-of-fit levels on the experimental data. The proposed exponential function has only two parameters compared to that of the exponential function in the literature which has four parameters. Therefore, the proposed exponential function is selected as the creep model of marble. This model is also related to a built-up combined spring-dashpot model known as the generalized Kelvin model. The model parameter values of the generalized Kelvin model are then calculated by the parameter relations that exist between the generalized Kelvin model and the proposed exponential function.

Review of the creep constitutive models for rocks and the application of creep analysis in geomechanics

“…An important consideration when suggesting empirical models is choosing the proper fitting function. The Power, Exponential, and Morgan Mercer Flodin growth functions are the most common fitting functions in the empirical models (Table 1) (Chen and Kulatilake 2015;Sun et al 2016). The Norton Power Law is also used frequently for modeling rock creep behavior, but this model cannot simulate the accelerated stage of rock creep (Liu et al 2021c).…”

“…The Bailey-Norton Law, or Time Hardening Law, is another empirical model utilized to model the first and steady-state phases of creep, and it is essential to adopt a positive initial time (May et al 2013). The Exponential function has been used to simulate the first and second phases of creep (Chen and Kulatilake 2015). As shown in Table 1, the Morgan Mercer Flodin growth is an asymmetrical sigmoidal function with four parameters (Sun et al 2016).…”

A Core Damage Constitutive Model for the Time-Dependent Creep and Relaxation Behavior of Coal

“…To further validate and popularize this core damage model, the creep testing data of a marble at a stress of 69 MPa in the uniaxial state [27] and the stress relaxation test data of a Cobourg limestone (Cbrg_16R) under uniaxial compression [6] were taken as examples, and the model curve and the experimental data are shown in Figure 6a,b. As seen, the unified core damage model curves could well describe the axial strain of marble at a stress of 69 MPa and the stress relaxation of the Cobourg limestone (Cbrg_16R) and the correlation coefficients were as high as 0.996.…”

A simplified log creep model for describing triaxial creep of mélange rocks

“…The creep behavior of the soft rocks reveals to include the decay, and steady and accelerated creep by many researchers [ [4] , [5] , [6] , [7] , [8] , [9] ]. The creep test of the hard rock was conducted to demonstrate the mechanical behavior of the rocks subjected to the triaxial loading condition [ [10] , [11] , [12] , [13] , [14] , [15] , [16] ]. The previous articles reported the experimental results to illustrate the creep behaviors of rocks subjected to various environmental conditions.…”